Asymptotic preconditioning of linear homogeneous systems of differential equations

We consider the asymptotic behavior of solutions of a linear differential system x ' = A(t)x, where A is continuous on an interval la, DC)). We are interested in the situation where the system may not have a desirable asymptotic property such as stability, strict stability, uniform stability, or linear asymptotic equilibrium, but its solutions can be written as x = Pu, where P is continuously differentiable on la, infinity) and u is a solution of a system u ' = B(t)u that has the property in question. In this case we say that P preconditions the given system for the property in question. (C) 2010 Elsevier Inc. All rights reserved.